基于GAMLSS模型的水文干旱指数研究——以玛纳斯河流域为例

doi:10.11821/dlyj020200927

摘要/Abstract

摘要：

传统的水文干旱指数是在一致性条件下确定的,而在非一致情况下水文干旱指数的识别精度受到质疑。特别是当全球气候发生剧烈变化的时候,应用合适的干旱指数可以增加干旱预警的精确度。一般在非一致情况下,通常会认为干旱指数的概率分布参数服从时间或者其他协变量的线性或者非线性变化。因此以玛纳斯河流域肯斯瓦特站为例,构建以时间为协变量的GAMLSS模型,建立非一致情况的标准化径流指数SRI_ns,并对比分析,讨论其适用性。结果表明：① 肯斯瓦特站1957—2014年期间,径流量的变化趋势比降水和气温的变化趋势更为明显,径流发生明显变化主要集中在秋季和冬季,降水全年各月的变化趋势不明显,气温则在春季和夏季变化较剧烈。② 通过对比研究区1957—2014年内有历史资料记载的历史干旱事件,SRI_ns对于研究区干旱事件的识别更准确,SRI_ns识别的严重干旱和极度干旱事件的发生频率要比SRI_s高。③ 通过游程理论识别出干旱特征变量,将干旱特征变量采用均匀分布随机化处理可以提高干旱历时序列的拟合精度。干旱特征变量序列的最优分布均为对数正态分布。④ SRI_ns和SRI_s的干旱特征变量的二维联合分布的最优Copula函数均为joe函数。通过对比干旱特征变量二维联合概率和重现期,SRI_ns可以缩小风险区间,增加干旱风险预警的精度,因此更适用于该研究区的干旱预测与风险评估。

关键词: GAMLSS模型, 非一致性, 标准化径流指数, Copula函数, 玛纳斯河流域

Abstract:

The traditional hydrological drought index is determined under the condition of nonstationary. However, the identification accuracy of this index is questioned, especially under the dramatical climate change, the application of appropriate drought index can increase the accuracy of drought warning. In general, under nonstationary conditions, the probability distribution parameters of drought index are generally considered to be subject to linear or nonlinear changes of time or other covariables. Therefore taking Kenswatt Station in the Manas River Basin as an example, we built a GAMLSS model with time as the covariable. The standardized runoff index SRI_ns in the case of nonstationary was established and compared with the standardized runoff index SRI_s in the case of stationary, and the applicability of SRI_ns was discussed. The results show that: （1） During 1957-2014, the variation trend of runoff was more obvious than that of precipitation and temperature at Kanswatt Station. The change of runoff was mainly concentrated in autumn and winter, while the change trend of precipitation was not obvious in each month of the year, while the change of temperature was more fluctuant in spring and summer. （2） By comparing historical drought events recorded in the study area from 1957 to 2014, SRI_ns can identify drought events more accurately. The frequency of severe drought and extreme drought events identified by SRI_ns was higher than that of SRI_s. （3） Drought characteristic variables were identified by Run theory. The fitting accuracy of drought duration series can be improved by using uniform distribution and randomization of drought characteristic variables. The results of cumulative probability show that the optimal distribution functions of the drought characteristic variable series of SRI_ns and SRI_s are lognormal distribution. （4） The optimal Copula function of the two-dimensional joint distribution of drought characteristic variables of SRI_ns and SRI_s is Joe function. By comparing the two-dimensional joint probability and return period of drought characteristic variables, SRINS can reduce the risk interval and increase the accuracy of drought risk warning, so it is more suitable for drought prediction and risk assessment in the study area.

Key words: GAMLSS model, nonstationility, standardized runoff index, Copula functions, Manas River Basin

陈伏龙, 杨宽, 蔡文静, 龙爱华, 何新林. 基于GAMLSS模型的水文干旱指数研究——以玛纳斯河流域为例[J]. 地理研究, 2021, 40(9): 2670-2683.

CHEN Fulong, YANG Kuan, CAI Wenjing, LONG Aihua, HE Xinlin. Study on hydrological drought index based on GAMLSS: Taking Manas River Basin as an example[J]. GEOGRAPHICAL RESEARCH, 2021, 40(9): 2670-2683.

图/表 14

图1

表1

表2

表3

图2

图3

表4

图4

图5

表5

表6

图6

图7

表7

参考文献 33

[1]	IPCC. Climate Change 2007: Synthesis Report. A Contribution of Working Groups I, II, and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Geneva: IPCC, 2007: 67-69.
[2]	Sarhadi A, Bum D H, Ausin M C, et al. Time-varying nonstationary multivariate risk analysis using a dynamic Bayesian copula. Water Resources Research, 2016, 52（3）:2327-2349. DOI: 10.1002/2015WR018525. doi: 10.1002/2015WR018525
[3]	丁一汇, 任国玉, 石广玉, 等. 气候变化国家评估报告（I）: 中国气候变化的历史和未来趋势. 气候变化研究进展, 2006, 2（1）:3-8.
	[ Ding Yihui, Ren Guoyu, Shi Guangyu, et al. National assessment report of climate change（I）: Climate change in China and its future trend. Advances in Climate Change Research, 2006, 2（1）:3-8.]
[4]	Mishra A K, Singh V P. A review of drought concept. Journal of Hydrology, 2010, 391（1-2）:202-216. DOI: 10.1016/j.jhydrol.2010.07.012. doi: 10.1016/j.jhydrol.2010.07.012
[5]	Mait R, Suman M, Verma E N K. Drought prediction using a wavelet based approach to model the temporal consequences of different types of droughts. Journal of Hydrology, 2016, 539（2）:417-428. DOI: 10.1016/j.jhydrol.2016.05.042. doi: 10.1016/j.jhydrol.2016.05.042
[6]	董前进, 谢平. 水文干旱研究进展. 水文, 2014, 34（4）:1-7.
	[ Dong Qianjin, Xie Ping. Advances in hydrological drought research. Journal of China Hydrology, 2014, 34（4）:1-7.]
[7]	Romero L, Perez-Sanchez M, Lopez PA. Improvement of sustainability indicators when traditional water management changes: A case study in Alicante （Spain）. AIMS Environ Sci. 2017, 4（3）:502-522. DOI: 10.3934/environsci.2017.3.502. doi: 10.3934/environsci.2017.3.502
[8]	熊立华, 江聪. 考虑非一致性的渭河流域设计洪水过程线研究. 水资源研究, 2015, 4（5）:109-119.
	[ Xiong Lihua, Jiang Cong. Designing flood hydrograph of the Weihe River considering nonstationarity. Journal of Water Resources Research, 2015, 4（5）:109-119.]. DOI: 10.12677/jwrr.2015.42013. doi: 10.12677/jwrr.2015.42013
[9]	Zou Lei, Xia Jun, Ning Like, et al. Identification of hydrological drought in Eastern China using a time-dependent drought index. Water, 2018, 10（3）:315-334. DOI: 10.3390/w10030315. doi: 10.3390/w10030315
[10]	温庆志, 姚蕊, 孙鹏, 等. 变异条件下淮河流域生态径流变化特征及驱动因子. 生态学报, 2020, 40（8）:2621-2635.
	[ Wen Qingzhi, Yao Rui, Sun Peng. Change characteristics and driving factors in nonstationary ecological flow condition across the Huai River Basin, China. Acta Ecologica Sinica, 2020, 40（8）:2621-2635.]. DOI: 10. 5846 /stxb201903080438. doi: 10. 5846 /stxb201903080438
[11]	王怡璇. 变化环境下滦河流域干旱演变驱动机制及定量评价研究. 天津: 天津大学博士学位论文, 2017: 104-141.
	[ Wang Yixuan. Driving mechanism and quantitative assessment of drought in Luanhe River Basin under changing environment. Tianjin: Doctoral Dissertation of Tianjin University, 2017: 104-141.]
[12]	李析男, 谢平, 李彬彬, 等. 变化环境下不同等级干旱事件发生概率的计算方法: 以无定河流域为例. 水利学报, 2014, 45（5）:585-594.
	[ Li Xinan, Xie Ping, Li Binbin, et al. A probability calculation method for different grade drought event under changing environment: Taking Wuding river basin as an example. Journal of Hydraulic Engineering, 2014, 45（5）:585-594.]. DOI: 10.13243/j.cnki.slxb.2014.05.010. doi: 10.13243/j.cnki.slxb.2014.05.010
[13]	方伟. 多变量视角下珠江流域洪旱灾害时变风险研究. 西安: 西安理工大学博士论文, 2020: 32-34.
	[ Fang Wei. Assessment time-varying risk of drought and flood from a multivariate perspective in the Pearl River Basin, China. Xian: Doctoral Dissertation of Xian University of Technology, 2020: 32-34.]
[14]	Wang Y, Li J, Feng P, et al. A time-depedent drought index for non-stationary precipitation series. Water Resources Management, 2015, 29（7）:5631-5647. DOI: 10.1007/s11269-015-1138-0. doi: 10.1007/s11269-015-1138-0
[15]	Javad Bazrafshan, Somayeh Hejabi. A Non-Stationary Reconnaissance Drought Index （NRDI） for drought monitoring in a changing climate. Water Resources Management, 2018, 32（8）:2431-2447. DOI: 10.1007/s11269-018-1947-z. doi: 10.1007/s11269-018-1947-z
[16]	M D Mamunur Rashid, Simon Beecham. Development of a non-stationary standardized precipitation index and its application to a south Australian climate. Science of the Total Environment, 2018, 657（1）:882-892. DOI: 10.1016/j.scitotenv.2018.12.052. doi: 10.1016/j.scitotenv.2018.12.052
[17]	邵进, 李毅, 宋松柏. 标准化径流指数计算的新方法及其应用. 自然灾害学报, 2014, 23（6）:79-87.
	[ Shao Jin, Li Yi, Song Songbai. A new standardized runoff index calculation method and its application. Journal of Natural Disasters, 2014, 23（6）:79-87.]. DOI: 10.13577/j.jnd.2014.0609. doi: 10.13577/j.jnd.2014.0609
[18]	陈伏龙, 张鑫厚, 冯平, 等. 基于非一致融雪洪水的水库漫坝模糊风险分析. 水力发电学报, 2018, 37（12）:22-32.
	[ Chen Fulong, Zhang Xinhou, Feng Ping, et al. Fuzzy risk analysis of dam overtopping under inconsistent snowmelt floods. Journal of Hydroelectric Engineering, 2018, 37（12）:22-32.]. DOI: 10.11660/slfdxb.20181203. doi: 10.11660/slfdxb.20181203
[19]	张正勇. 玛纳斯河流域产流区水文过程模拟研究. 石河子: 石河子大学博士论文, 2018: 28-29.
	[ Zhang Zhengyong. Modeling hydrological processes in main runoff generating area of Manasi River Basin, Xinjiang. Shihezi: Doctoral Dissertation of Shihezi University, 2018: 28-29.]
[20]	郭飞. 新疆生产建设兵团第八师石河子市统计年鉴. 北京: 中国统计出版社, 2019: 58-64.
	[ Guo Fei. Shihezi Statistical Yearbook of the 8th Division of Xinjiang Production and Construction Corps. Beijing: China Statistics Press, 2019: 58-64.]
[21]	王义忠. 玛纳斯河流域水利志. 石河子: 石河子水电局自治区玛管处, 2002: 23-25.
	[ Wang Yizhong. Water Conservancy of the Manas River Basin. Shihezi: Shihezi Water and Electricity Bureau Autonomous Region Management Department, 2002: 23-25.]
[22]	史玉光. 中国气象灾害大典:新疆卷. 北京: 气象出版社, 2006: 138-152.
	[ Shi Yuguang. China Meteorological Disasters: Xinjiang Volume. Beijing: Meteorological Press, 2006: 138-152.]
[23]	Shukla S, Wood A W. Use of a standardized runoff index for characterizing hydrologic drought. Geophysical Research Letters, 2008, 35（2）:226-236. DOI: 10.1029/2007GL032487. doi: 10.1029/2007GL032487
[24]	Rigby R A, Stasinopoulos D M. Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society: Series C （Applied Statistics）. 2005, 54（3）:507-554. DOI: 10.1111/j.1467-9876.2005.00510.x. doi: 10.1111/j.1467-9876.2005.00510.x
[25]	Stasinopoulos D M., Rigby R A. Generalized Additive Models for Location Scale and Shape （GAMLSS） in R. Journal of Statistical Software, 2007, 23（7）:1-46. DOI: 10.18637/jss.v023.i07. doi: 10.18637/jss.v023.i07
[26]	江聪, 熊立华. 基于GAMLSS模型的宜昌站年径流序列趋势分析. 地理学报, 2012, 67（11）:1505-1514.
	[ Jiang Cong, Xiong Lihua. Trend analysis for the annual discharge series of the Yangtze River at the Yichang hydrological station based on GAMLSS. Acta Geographica Sinica, 2012, 67（11）:1505-1514.]. DOI: 10.11821/xb201211007. doi: 10.11821/xb201211007
[27]	Li J Z, Wang Y X, Li S F, et al. A nonstationary standardized precipitation index incorporating climate indices as covariates. Journal of Geophysical Research Atmospheres, 2016, 120（23）:12082-12095. DOI: 10.1002/2015JD023920. doi: 10.1002/2015JD023920
[28]	Nelson R B. An Introduction to Copulas. New York: Springer, 1999: 671-672.
[29]	Mann H B. Nonparametric tests against trend. Econometric: Journal of the Econometric Society, 1945, 13（3）:245. doi: 10.2307/1907187
[30]	Kendall M G. Rank Correlation Measures. London: Charles Griffin, 1975: 505-506.
[31]	郑锦涛. 气候变化驱动下玛纳斯河山区径流演变规律研究. 石河子: 石河子大学硕士论文, 2018: 19-20.
	[ Zheng Jintao. Study on the law of runoff evolution in Manas river mountainous area driven by climate change. Shihezi: Mater Dissertation of Shihezi University, 2018: 19-20.]
[32]	Vandenberghe S, Verhoest N E C, De Baets B. Fitting bivariates copulas to the dependence structure between storm characteristics: A detailed analysis based on 105 year 10 min rainfall. Water Resources Research, 2010, 46（1）:W01512. DOI: 10.1029/2009WR007857. doi: 10.1029/2009WR007857
[33]	De Michele C, Salvadori G, Vezzoli R, et al. Mutivariate assessment of droughts: Frequency analysis and dynamic return period. Water Resources Research, 2013, 49（10）:6985-6994. DOI: 10.1002/wrcr.20551. doi: 10.1002/wrcr.20551

SRI	≥2.00	1.99~1.50	1.49~1.00	0.99~0.00	0.00~-0.99	-1.00~-1.49	-1.50~-1.99	≤-2.00
分类	极度湿润	非常湿润	中等湿润	正常	轻微干旱	中等干旱	严重干旱	极度干旱
等级	1	2	3	4	5	6	7	8

月份	径流		降水		气温
月份	Kendall 统计值	趋势性	Kendall 统计值	趋势性	Kendall 统计值	趋势性
1	3.85	显著	0.83	不显著	1.29	不显著
2	4.49	显著	1.87	不显著	0.60	不显著
3	3.55	显著	1.14	不显著	1.87	不显著
4	0.08	不显著	0.97	不显著	3.92	显著
5	0.09	不显著	0.07	不显著	3.57	显著
6	0.97	不显著	1.31	不显著	5.33	显著
7	1.77	不显著	0.06	不显著	5.72	显著
8	1.93	不显著	0.40	不显著	5.94	显著
9	4.14	显著	0.41	不显著	4.63	显著
10	3.16	显著	0.53	不显著	4.82	显著
11	2.07	显著	1.31	不显著	2.66	显著
12	1.44	不显著	2.54	显著	0.40	不显著
年值	2.97	显著	0.20	不显著	6.00	显著

月份	μ		σ		均值	方差	偏态系数	峰态系数	Filleben 系数
月份	a₀	a₁	b₀	b₁	均值	方差	偏态系数	峰态系数	Filleben 系数
1	-8.9839	0.0062	4.5104	-0.0022	0.0002	1.0206	0.1410	2.4667	0.9917
2	-9.6650	0.0065	0.1511		-0.0003	1.0175	0.4524	3.0384	0.9892
3	-12.3800	0.0078	0.1561		-0.0002	1.0175	0.3428	3.3299	0.9872
4	-7.0489	0.0051	0.1271		-0.0005	1.0175	0.3623	2.7879	0.9865
5	3.6699		0.1971		-0.0004	1.0175	0.3828	2.6598	0.9864
6	4.6642		0.2023		-0.0005	1.0175	0.4472	3.7115	0.9859
7	-1.3909	0.0035	-5.3093	0.0028	-0.0004	1.0180	0.0896	2.1885	0.9939
8	-1.1270	0.0035	-4.7330	0.0025	-0.0009	1.0185	0.4846	2.3550	0.9793
9	-5.9108	0.0058	-3.6798	0.0019	-0.0006	1.0186	0.4082	2.5795	0.9880
10	-11.1558	0.0082	0.2272		-0.0005	1.0174	0.3990	2.8088	0.9850
11	-24.4300	0.0143	0.2452		-0.0005	1.0174	0.2950	2.2722	0.9880
12	-3.3197	0.0036	0.1466		-0.0001	1.0175	0.2077	2.8631	0.9912

干旱年份	起始时间年-月	SRI_s		SRI_ns
干旱年份	起始时间年-月	S	D	S	D
1961	1961-6	3.23	4	4.44	4
1970	1970-1	7.42	11	7.84	10
1977	1977-2	15.06	16	17.61	15
1983	1983-2	27.14	26	37.01	26
1990	1990-8	22.63	28	47.17	33
1997	1997-9	0.00	0	6.51	8
1999	1999-3	0.33	3	1.52	4
2006	2006-7	0.00	0	3.40	5
2009	2008-9	2.52	6	10.50	15

干旱指数	干旱特征变量	边缘分布函数	K-S统计值	分布参数值
SRI_ns	干旱历时（月）	对数正态分布	0.1225	μ=1.6219, σ=0.8299
SRI_ns	干旱烈度	对数正态分布	0.1056	μ=1.0858, σ=1.2100
SRI_s	干旱历时（月）	对数正态分布	0.0787	μ=1.6878, σ=0.8165
SRI_s	干旱烈度	对数正态分布	0.1038	μ=0.7858, σ=1.3703